I played a character like this once. She was very young, and had witnessed the (rather brutal) deaths of her parents at an even younger age. As such, she was very hesitant to open up to or trust strangers. And in this particular campaign, even the other PCs were strangers, only having met one another at the onset of the campaign.
My character felt confident not when she was doing something she was good at, but instead only really opened up to "her mother" -- that is, she had a pendant that was the only thing left behind from her parents, so she often "saw" her mother and would tell her things she wasn't really prepared to tell the party. Her mother was more like an imaginary friend in this regard, but it helped a lot to communicate to the other PCs.
For example, if she spotted a trap or sensed some kind of danger, rather than telling the PCs directly, they might hear her whisper to her mother, "Be careful here Mom; whoever built this place doesn't want us seeing what's inside."
Depending on what your character is "good at", you could use that as a conduit to communicate to the party or perhaps others. If her hobby is something like whittling, then perhaps she can only truly communicate effectively while she focuses on her carving, making no eye contact with the person to whom she's speaking, thus making it very awkward to talk to her.
Avoiding eye contact is a good way to convey that a character is nervous or uncomfortable. Other possibilities might be that the character develops specific nervous habits that come up often when she's in a social situation. This can range from serious, realistic nervous habits (such as fidgeting a lot, biting fingernails, always being distracted by rummaging through her sack, stopping sentences halfway through because she feels like she's saying something wrong/stupid) to more fun, light-hearted habits (such as referring to things by using unconventional names that make her feel more comfortable [calling a mermaid character "Fishy One" if she's kinda childish; calling a werewolf character "Homo Lupus" if she's super intelligent], specifically asking characters to turn their backs to her when she addresses them).
Also, as has been mentioned before: Just because your character isn't comfortable speaking all the time, doesn't mean she can't act all the time. As you're walking through the woods, maybe your character spots a pitfall trap that your party is about to walk into. Rather than shouting a warning, she might just pick up a nearby stone and throw it onto the trap, causing it to collapse and thereby warning the others.
And lastly, being "shy and quiet" can often be played as an advantage in many social situations. If your character is at all smart and resourceful, it shouldn't be difficult for her to sneak away from the party unnoticed and pull off some kind of covert reconnaissance while the others keep the NPCs distracted by being social. This is one of my favorite things to do with a quiet character -- help the party out in ways that they don't even notice until a couple of sessions later, then leave them wondering how in the world it happened.